A Hybrid Nash Min-Max Approach for Solving Continuous Static Games

Authors

Yousria A. Elnaga, Department of Basic Science, Higher Technological Institute Tenth of Ramadan City, EgyptFollow
Abdullah S. Shalaby, Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, EgyptFollow
Ali S. Shehab, Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

This paper addresses a novel structure of continuous static games (CSGs) called hybrid continuous static games (HCSG). These types of games are based on the fact that the game is presented as a hybrid game between multiple players playing independently using Nash equilibrium solutions (NES) and others playing according to a secure concept using Min-Max solutions (MMS). A Nash Min-Max approach was established to solve such genre games. Also, an algorithm for solving Nash Min-Max hybrid continuous static games (NMMHCSG) has been outlined in clear steps. Moreover, a realistic application of four firms selling replaceable products and seeking to maximize their profits was presented to demonstrate the steps of the algorithm.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140611

Recommended Citation

A. Elnaga, Yousria; S. Shalaby, Abdullah; and S. Shehab, Ali (2020) "A Hybrid Nash Min-Max Approach for Solving Continuous Static Games," Applied Mathematics & Information Sciences: Vol. 14: Iss. 6, Article 11.
DOI: http://dx.doi.org/10.18576/amis/140611
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss6/11